EVENTS

Ockham and Twain

One of the things that used to bother me about Ockham’s Razor was the almost coincidental way it “just so happens” that the simplest solution is most likely to be correct. Oh really? How convenient for us simple-minded investigators! Are you sure there isn’t some kind of scam going on here?

As it turns out, there isn’t. In a world where “true” and “false” are consistently meaningful terms, the law of parsimony will always apply. The correct explanation will be the simplest explanation that accounts for all the facts.

To understand why this is so, we just need to consider what “truth” is. Truth is defined by its consistency with reality, and reality is consistent with itself. Conversely, falsehoods are not consistent with reality, by definition, and not infrequently fail to be consistent even with themselves.

When we try to explain something—as opposed to superstitiously attributing it to magical causes—our goal is to discover the truth, which means we want an explanation that’s consistent with reality. Any time we fail, we produce an explanation that contains inconsistencies with reality and possibly with itself as well. These inconsistencies will also require explanation, which in turn will make our original, incorrect explanation more complicated. The simplest explanation will be the one that has the fewest such complications, and the correct explanation will be the one that has zero additional inconsistencies to explain. Thus, the simplest explanation is the most likely to be correct because the nature of error makes erroneous explanations inherently more complex.

As Mark Twain put it, it’s easier to tell the truth because there’s less to remember. True explanations have the advantage of reflecting the inherent self-consistency of reality itself, and not uncommonly have the characteristic of being consistent with real-world evidence that you don’t even know yet. Thus, for example, Darwin’s theory of evolution turns out to be consistent with discoveries that Darwin himself knew nothing about, like DNA and radiometric dating methods, whereas creationist speculations keep raising new inconsistencies with each new “explanation” for why we don’t see stars being created six to ten thousand light years away, or how so many modern, surviving species can be descended from small numbers of “kinds” aboard the ark if there’s no such thing as descent with variation from common ancestral species.

This fact, plus an understanding of how superstition and rationalization work, give us an opportunity to test what we think we know, and examine our beliefs for evidence that we might, perhaps, be clinging to false ideas. But that’s going to be tomorrow’s post.

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Some of these “theories” begin to resemble ancient inner tubes: more patch than original rubber.

However, it’s good to keep in mind that we can discover truth by circuitous means, too. When I was a kid I transferred schools mid-term. My new school was heavy into long division, something we hadn’t even begun back at my old digs. Well, I was thoroughly confused. I got the idea of what division was all about. What I couldn’t wrap my head around was the procedure for finding the answer that was being taught to me. In desperation I contrived my own, rather convoluted process. Oh, it worked, if by “worked” we mean it gave me the right answer. I just had to work twice as hard to get where I wanted to go.

Likewise, I think we sometimes find truth by tortuous means, making it seem more complicated than it needs to be. Complication, then, doesn’t necessarily imply untruth. Perhaps it’s only that we haven’t found the more direct route to it yet.

Isn’t that claim verifiably false? There have been huge numbers of theories that were accepted as they seemed to explain the data parsimoniously – only to be disproven when new facts emerged. I think you’re conflating ‘error of fact’ with ‘error in reasoning'; even a perfectly reasoned, rational, and parsimonious account can be factually wrong in the face of inadequate data.

Ah, but the only way we find out if it’s false is if it turns out to be inconsistent with the facts. The true explanation will necessarily be the simplest explanation that covers ALL the facts, and therefore given two explanations that cover the same set of facts, the simpler one is more likely to be true. Granted, in the face of incomplete information, we’re talking probabilities rather than certainties, and new facts may reveal inconsistencies that were previously unsuspected. Nevertheless, in the absence of any known facts contradicting the simpler hypothesis, we have greater justification for adopting the simpler explanation than we do for preferring the one that multiplies entities unnecessarily.

Thanks for writing this, Deacon! I’ve been reading you for years, and you frequently raise this point “reality is consistent with itself”, but it’s really nice to have this useful tool explained so clearly in one place. Definitely one for the favorites file.

What I couldn’t wrap my head around was the procedure for finding the answer that was being taught to me. In desperation I contrived my own, rather convoluted process. Oh, it worked, if by “worked” we mean it gave me the right answer. I just had to work twice as hard to get where I wanted to go.

The thing is that the underlying reality we’re discussing is inherently self-consistent. That means if you have an explanation that’s consistent with the facts you already know, any new facts are more likely to be consistent with your current explanation than inconsistent. The reason why it’s newsworthy when new facts force a re-evaluation of existing theories is precisely because this outcome is (relatively speaking) so rare. And even then the new facts are more likely to force a refinement of an existing theory than a complete overthrow. So other things being equal, the most parsimonious explanation is still more likely to be closer to the truth than any explanation that needlessly multiplies agencies.

That’s a good way to approach it from the perspective of what we think we know, and it’s a good guide for evaluating what we think we know in the light of the facts we know. I’m approaching it from the other direction however. I’m saying the most correct explanation—whether anyone knows that explanation or not—is also going to be the simplest, because it will have the fewest actual discrepancies to account for. You can’t have a negative number of discrepancies, so the smallest possible number is zero, which is the number of discrepancies that the correct explanation will have. All incorrect explanations will be incorrect by virtue of having one or more discrepancies with actual fact, and therefore the correct explanation will necessarily be simpler than all incorrect ones.

Occam: “plurality should not be posited without necessity” (Ref. Wikipedia)

This is advice for thinkers (not scientists in particular). If you have 2 ideas that do the same job and one of them is easier to use then stick with the easier one. This will make your life easier. It’s up to each thinker to have his own concept of “easier”. In other words, just because an idea is harder to use doesn’t make it better. The merit of an idea must be judged by what it achieves.

Occam did not posit a principle to guide physicists in choosing which hypothesis is more correct or more likely to be correct. There is no definition in physics for “simple”. That is a concept for human minds and it varies from one person to another. Occam’s advice to physicists is: express your idea in a way that takes the least effort for you personally without sacrificing the usefulness of the idea (ex. accuracy of the predictions). Two physicists could write down equivalent theories (equivalent outcomes) in ways that they find personally the simplest.

The above explanation makes sense in Occam’s context and makes it useful advice to everyone throughout time.